# Worksheet on Rational Numbers

Practice the questions given in the worksheet on rational numbers.

We know, numbers that can be expressed in the form x/y, where y is a non - zero integer and x is any integer are called rational numbers.

The questions are based on rational number, useful results on rational number, positive rational number and negative rational number.

1. Write down the numerator of each of the following rational numbers:

(i) (-7)/5

(ii) 15/(-4)

(iii) (-17)/(-21)

(iv) 8/9

(v) 5

2. Write down the denominator of each of the following rational numbers:

(i) (-4)/5

(ii) 11/(-34)

(iii) (-15)/(-82)

(iv) 15

(v) 0

3. Write down the rational number whose numerator is (-3) × 4, and whose denominator is (34 - 23) × (7 - 4).

4. Write the following rational numbers as integers:

17/1, (-23)/1, 35/1, (-77)/1, 91/1.

5. Write the following integers as rational numbers with denominator 1:

-19, 27, 71, -101.

6. Write down the rational number whose numerator is the smallest four digit number and denominator is the largest five digit number.

7. Separate positive and negative rational numbers from the following rational numbers:

(-5)/(-7), 12/(-5), 7/4, 13/(-9), 0, (-18)/(-7), (-95)/116, (-1)/(-9)

8. Which of the following rational numbers are positive?

(i) (-8)/7         (ii) 9/8          (iii) (-19)/(-13)       (iv) (-21)/13

9. Which of the following rational numbers are negative?

(i) (-3)/7       (ii) (-5)/-8        (iii) 9/(-83)        (iv)  (-115)/-197

10. Which is the following statement are true or false?

(i) Every whole number is a rational number.

(ii) Every integer is a rational number.

(ii) 0 is a whole number but it is not a rational number.

Answers for the worksheet on rational numbers are given below to check the exact answers of the above questions on rational number.

1. (i)  -7

(ii) 15

(iii) -17

(iv) 8

(v) 5

2. (i) 5

(ii) -34

(iii) -82

(iv) 1

(v) any non zero integer

3. (-12)/33

4. 17, -23, 35, -77, 91

5. (-19)/1, 27/1, 71/1, (-101)/1

6. 1000/99999

7. Positive rational numbers: (-5)/(-7), 7/4, (-18)/(-7), (-1)/(-9);

Negative rational numbers: 12/(-5), 13/(-9), (-95)/116

8. (ii) 9/8

(iii) (-19)/(-13)

9. (i) (-3)/7

(iii) 9/(-83)

10. (i) true

(ii) true

(ii) false

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Rational Numbers

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

Equivalent form of Rational Numbers

Rational Number in Different Forms

Properties of Rational Numbers

Lowest form of a Rational Number

Standard form of a Rational Number

Equality of Rational Numbers using Standard Form

Equality of Rational Numbers with Common Denominator

Equality of Rational Numbers using Cross Multiplication

Comparison of Rational Numbers

Rational Numbers in Ascending Order

Representation of Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Addition of Rational Numbers

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

To Find Rational Numbers